Determine maximum value of this solution for t>0

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The discussion revolves around finding the maximum value of the function y = e^(-t) - e^(2t) for t > 0. Participants clarify that the maximum occurs at t = 0, raising questions about the intent of the original question. It is suggested that the question aims for students to identify zero as a critical point and apply derivative tests to confirm the maximum. The conversation emphasizes the importance of demonstrating understanding through critical number analysis and derivative testing. Ultimately, the focus is on the mathematical process of determining maximum values in calculus.
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The equation is y=e^(-t)-e^(2t)

It says: Determine maximum value of this solution for t>0 and the value of t where this maximum occurs.

Doesn't the maximum occur at 0? So what is the question asking?
 
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NINHARDCOREFAN said:
Doesn't the maximum occur at 0?

Yes.

So what is the question asking?

If I were asking the question, I would expect my students to show that zero is a critical number of f(x), and then to use either the first or second derivative test to demonstrate that there is indeed a maximum at that point.
 

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